Power system protective relaying by time-coordinated sampling and calculation

ABSTRACT

A method of controlling the operation of a breaker in a transmission line by first monitoring the current and if the current exceeds a prescribed limit, measuring a sampling of the voltage on the line when the current is at zero and dividing this value by the maximum current on the line to obtain a first quantity which is added to a second quantity obtained by measuring a sampling of the voltage when the current is at its maximum value and dividing this voltage by the maximum current. The previous calculations will provide a measure of impedance since the voltage when the current is zero is equal to Vm sin phi while the voltage when the current is at maximum is equal to Vm cosine phi and impedance in a rectangular coordinate representation is: z R jX Vm cosine phi /Im + j(Vmsin phi /Im). This apparent impedance is then compared against relay characteristics which are implemented in a programmed general purpose computer and in the event the apparent impedance lies within the relay characteristic zone, the associated breaker is tripped.

United States Patent Inventors Appl. No. Filed Patented Assignee POWERSYSTEM PROTECTIVE RELAYIN G BY TIME-COORDINATED SAMPLING AND 3,237,1002/1966 Chalfinetal. 3,340,434 9/1967 Riebs ABSTRACT: A method ofcontrolling the operation of a breaker in a transmission line by firstmonitoring the current and if the current exceeds a prescribed limit,measuring a sampling of the voltage on the line when the current is atzero and dividing this value by the maximum current on the-line toobtain a first quantity which is added to a second quantity ob- 5 2: gthis voltage by the [52] [LS-Cl. 317/27, axim m current, The previouscalculations will provide a 235/ 1 1- 235/ 151.31, 317/36, 324/57measure of impedance since the voltage when the current is [51] Int. Cl"02h 3/40 z ro i ual to V sin (I) while the voltage when the current is[50] Field ofsearch 317/36 ((1), at maxi um is equal to V cosine (l) andimpedance in a rectangular coordinate representation is: z R+jX V,,cosine I /I +j(V sin 1 /l Thisapparent impedance is then comparedagainst relay characteristics which are implemented [56] References cuedin a programmed general purpose computer and in the event UNITED STATESPATENTS the apparent impedance lies within the relay characteristic2,595,675' 5/1952 Jaynes 324/57Z I zone, the associated breaker istripped.

31 20 f SIN SAMPLE M "3 56 l r29 5 AND L f;

28 L ll ll ll HOLD To A/D CONVERTER 23 DELAY ,50 22 AND COMPUTER rr/Z pu n n 4. 58 cl fiNG 2? 32 DELAY (5 DHQECTOR Z INTERRUPT F0? COMPUTER V003 i r 39 42 M i 2 v cos b .a 41 V SIN smiguz v cos '2 i" HOLD -To A/DAND COMPUTER ZZ v SIN "1 F 2 V=V S|N(a VMOOS 43 M L i r -v S|N P SAMPLEu 44 1 AND l f HOLD TO A/D AND COMPUTER .PATENYEUIARJSIQTI- IGSSS-JBS'snmgn FIGJ ' FIG.-5(B) INVENTORS ROBERT C. DURBECK PATRICK E. MANTEYATTORNEY PATENTEU MR 9 ISTI T0 CIRCUITBREAKER SHEET 2 OF 3 ,51 M r n I'5 51 sm w R f. M SAMPLE n 5 I AND k 2L HOLD D T0 A/D CONVERTER DELAY,50 22 AND COMPUTER cg fuc I DELAY I Z INTERRUPT FOR DETECTOR 26COMPUTER v c0s r VMCOS (53 -41 v sm I SAAIwBLE v cosw "2 I F HOLD -ToA/D AND coMPuTER R W2; 2 v SM n 2| v-vnSlM m) VMOOS 43 M 1 R r -V S|N FSAMPLE M 44 AND f HOLD T0 MD AND COMPUTER INTERRUPT INITIAL 1 GENERATEHOUSEKEEPING ADDRESS LOAD I I0 MASKI/O 1 OF ROUTINE COMPARE WITH STOREINST. REG. FOR THIS THRESHOLD STORE INDEX REG INTERRUPT STORE STATUS vcos 4 v saw 5 R X M v cos, v suw, .l m MEMORY M IM m MEMORY EXIT v 8HOUSEKEEPING FAULT LOAD INDEX REG" IMPLEMENT 6 FAULT LOADINST. REG.RELAY 7 LOAD STA us FIG, 4 CHARACTERISTIC X10 UNMASK 1 AIEIIIEIIIIII9|97| 3.569.785

SHEET 3 0F 3 INTERRUPT I .T

V I INITAL HOUSEKEEP'NG' 6. IMPLEMENT RZELAY cH xRAcTER IsTIc MAS-K W Iv (a) (CIRCLE) n (R-U) (x-v STORE ms. REG. 1 1 SUBTRACT v sToRE STATUSSTORE x-v STORE INDEX REG. SQUARE x-v sToRE ACCUM. STORE x-v sToRESTATUS v LOAD R I I SUBTRA'CT'U A STORE R-U 2. GENERAAYTE ADDRESS ISQUARE LOAD ADD (x-w S COUNT COMPARE WITH 0 CONDITIONAL BRANCH 3.coIvIPARE IM WITH THRESHOLD 7. OPERATE BREAKER LOAD: IM 0 'M COMPAREwITH I 1 8. ExIT HOUSEKEEPING I LOAD INDEX REG.

- I LOAD INS. REG. TSX I LOAD STATUS M UNMASK l/O o INYERT l/I BLQCKI}.STORE VIM ALTERNATE MULT BY v cos STORE R 6. STRAIGHT-LINECHARACTERISTIC A COMPARE x mm zERo Q I COMPARE x mm x ll l1 5. coMPuTE xLOAD R LQADIAM MULTIPLY BY P MULT BY v sII I ADD X sToR x COMPARE WITHP0 .5? If .I, Q.1.;

LOAD R' MULTIPLY BY w RW1+X W0 ADD x .I FIG COMPARE WITH w POWER SYSTEMPROTECTIVE RELAYING BY TIME- COORDINATED SAMPLING AND CALCULATIONBACKGROUND OF INVENTION 1. Field of Invention This invention relates tothe control of the breakers in transmission lines in general, and moreparticularly, relates to a technique of determining apparent impedancefollowed by subsequent relay action without determining trigonometricfunctions of the sine and cosine of the relative phase between thevoltage and the current.

2. Description of Prior Art In the prior art the most widely usedcontrol for operating breakers is based on a measure of apparentimpedance as seen by the relay. The relays are primarilyelectromechanical devices in which opposing torques are utilized andwhen the torque associated with impedance exceeds the biasing torque,the breaker is tripped. Each of the relays on a transmission line mustbe set by a maintenance man using relatively complex equipment.

The electromechanical type of relayhas not been entirely satisfactory inthe past in that it has been the cause of recent massive power failures.In one power failure a number of relays were inadvertently set to tripon a relatively low impedance and since the dispatcher did not know thathis control strategy was approaching the threshold of the settings hecould not take corrective action and the relays tripped and a surge ofpower was placed on other lines which in turn caused a cascading effect.In another instance, the relays again were incorrectly set such thatthey did not trip when the control strategy of the dispatcher reached acritical thermal limit and one transmission line sagged onto anotheragain causing a cascading of breaker trips and a resultant surge ofpower causing further cascading.

For optimum control of faults on a transmission line, the setting ofeach of the relays must be known by the dispatcher so that he canregulate his control strategy in accordance with the settings and,additionally, it would be further desirable if the dispatcher couldalter the settings of the relays. That is, under different conditions,the dispatcher might want the relays to trip differently to alleviate,for instance, the problems associated with a line exceeding itsthermallimit.

Additionally, it would be desirable if the speed of action of the relayscould be increased, since the electromechanical relays currently in useare relatively slow in that they measure an average or RMS value and,additionally, have inertia to overcome. Thus, the typical operating timeof an electromechanical relay is on the order of several cycles.

Another problem associated with electromechanical relays is that ofcomplexity in the event that a characteristic other than a circularcharacteristic is to be implemented. That is, with electromechanicalrelays a circular impedance zone is usually implemented since this isthe least complicated characteristic and when the impedance'falls withinthis circular zone, the breaker is tripped. One problem associated withthe circular characteristic is that the impedance may rotate or movearound during transient swings between generators and cause a breakertrip which should not have occurred since no fault has occurred. Toalleviate this problem, a bias is usually placed on theelectromechanical relay so that the circle zone is moved further up intothe first quadrant. Also, to further alleviate false trips, oftenblinders are added to the circular impedance zone. The more refinedpatternthat the zone takes the more complex the relay is sinceadditional torque coils must be added to the relay to define the morecomplicated impedance zones. Consequently, it is desirable not only tobe able to implement any desired relay characteristic, but it is furtherdesirable to implement these relay characteristics in a straightforwardsimple and foolproof manner such that when the apparent impedance fallswithin the danger zone, relay action will immediately take place.

Solid State analogue equipment also exists for relaying based on ameasurement of apparent impedance and simple boundaries for relay actionare implemented by analogue comparisons. Both these devices and theelectromechanical relays suffer from a lack of flexibility and theirrelay characteristics cannot be changed remotely.

SUMMARY OF INVENTION Briefly, there is provided a control technique foruse in controlling the tripping of breakers in transmission lines whenthe apparent impedance falls within a precise zone. In the presenttechnique the line current is first measured to determine whether itexceeds a prescribed limit. In the event that the cur rent does notexceed the prescribed limit, no further control action is taken, but thecurrent value is stored by writing over the previous value in memory.Similarly, the voltage on the line is measured by sampling at the timethe current is at zero, which provides a measure of V sin I and thisquantity is stored and the voltage is measured by sampling when thecurrent is at its maximum value which gives a measure of V cos 1 andthis quantity is stored. Both of these values are also written over thepreviously measured values. In the event the current exceeds theprescribed limit, further control action must be taken. To accomplishfurther control, the quantities representing V,,,sin 1 and V,,,cosl areeach divided by the maximum current and the result added, which providesa measure of apparent impedance without requiring the conventional timemeasure between current and voltage to obtain the relative phase anglebetween current and voltage followed by the determination of the sineand cosine of the phase angle. The apparent impedance is then comparedwith the relay characteristics in a programmed general purpose computerto determine whether the apparent impedance falls within the relaycharacteristics. In the event that the impedence falls within the relaycharacteristic, the breaker is tripped.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an overall block diagramillustrative of a transmission line and breaker along with the controlcircuitry for activating the breaker in the event that the impedance onthe portion of the line with which the breaker is associated fallswithin a prescribed relay characteristic set by the dispatcher;

FIG. 2 is a waveform illustrative of the novel method of obtainingquantities in the subject invention which are used for a directdetermination of impedance;

FIG. 3 is a block diagram along with associated waveforms of a deviceutilized to obtain the quantities designated in FIG. 2 whereby a directreading of impedance can be obtained;

FIG. 4 is a generalized flow chart of the actions taken on an interruptbasis by a computer to accomplish control in accordance with theapparent impedance and the relay characteristic implemented;

FIG. 5a is a diagram of a circular impedance zone;

FIG. 5b is a diagram of a line impedance zone; and

FIG. 6 is a detailed flow chart of the actions to be taken to effectcontrol based on the impedance of the line as considered in conjunctionwith both a circular impedance pattern and a linear or line impedancepattern.

DESCRIPTION OF THE PREFERRED EMBODIMENT Refer first to FIG. 1 in whichis shown a source I which may be the power source such as the generatorstation, or may be a transmission line. The source is connected througha breaker 2 to a transmission line 3. Connected to the transmission line3 is a voltage and current sampling means 4 which provides measures ofmaximum current, voltage when the current is jat zero and voltage whenthe current is at its maximum value, to the analogue to digitalconverter 5 which in turn provides a digital representation of thesequantities to the computer Q. In the preferred embodiment hereinafterdescribed, in the computer 6, the relay characteristic is implemented,the apparent impedance calculated and a comparison of the two made todetermine if the impedance falls within'the characteristic. Adispatching station 7 communicates with the computer 6 and rovides relaycharacteristics which are to be implemented. The computer 6 is connectedalong line 8 to the breaker 2 such that the breaker 2 can be operated inthe event that, as hereinafter described, the impedance of the line 3falls within the relay characteristics set by dispatching station 7.

While in FIG. 1 there is shown a single transmission line and breakerand a single relay characteristic implementing and comparison means 6,this was done for simplicity and it should be understood that a numberof transmission lines will be associated with a single programmedcomputer which effects control over the breakers associated with each ofthe transmission lines.

In the normal operation of a relay in a transmission line, the relayoperates as previously described on the apparent impedance of itsassociated line and, if the apparent impedance falls within apreselected zone, which is often circular, the relay will cause thebreaker to open. Present electromechanical relays convert RMS voltageand current measurements into corresponding torques which in conjunctionwith bias torques yield boundaries for relay action. Solid stateanalogue equipment also exists for relaying based on impedancemeasurements and simple boundaries for relay action are implemented byanalogue comparisons. Complicated characteristics are achieved aspreviously described by use of multiple relays or blinders. Theshortcomings of all of these techniques are that they lack flexibilityand are difficult to change as far as their characteristics from aremote location.

In attempting to overcome the problem of lack of flexibility, applicantsdecided that since a computer could economically be made available ateach major substation, the computer could monitor the impedance of eachof the relays and, provided the impedance of the line fell within therelay characteristic, the relay could be tripped. However, the problemof calculating impedance was not easily overcome. The first approachtaken was to measure peak voltage and peak current, which is relativelystraightforward, and then determine the relative phase. Basically, theapproach involved taking the time when the voltage crossed zero and thetime that the current crossed zero and converting this time to an angle.This angle was then, by means of hardware, converted into the sine andcosine of the angle and the impedance obtained in accordance with thefollowing equation:

The above technique was relatively complicated in that while it wasrelatively simple to detect when the voltage crossed zero and when thecurrent crossed zero, a timer was required and a conversion of themeasured time to an angle had to be made. Also, a hardware device forproviding a trigonometric function (sin, cos 1 was necessary. The needfor this relatively complex hardware at each of the substations madethis method of calculating apparent impedance impractical.

Applicants overcame this problem by a simple technique which isgraphically illustrated in FIG. 2. In FIG. 2 the current is plotted as afunction of time in the upper plot (I= I,, sin wt) and the voltageisplotted as a function of time (V V sin rut-HI be seen that when thecurrent passes through zero, the voltage at that time is equal to V, sinI while when the current is at its maximum the voltage is equal to V,"Cos I Thus, if a measure ofthe voltage is taken when the current is atits maximum and zero values and these measurements stored and themaximum current obtained, the impedance that the relay sees can bedetermined directly. That is, since Z=R+j =V cos Pl I,, jV sin I /I,,,,all of the quantities required to determine impedance are at hand. Nohardware for determining the angle or the trigonometric function of theangle, i.e., sinecosine, is required. Instead these values can be takendirectly. Thus, R and X can be determined directly without the use oftrigonometric functions. The value obtained when the current goesthrough zero is V, sin I with the sign being positive when the currentis going negative and the sign being negative when the current is goingpositive. If the voltage is again sampled one-fourth of a cycle later,(1r/2), the current is at that time at its maximum and the quantities iV, cos 1 and t I,,, are obtained with the same sign consideration asabove. If we let r V,, sin 1 r 'V,,, cos I "a =iI then which can becalculated by one fixed point inversion (1 /r;,) and two fixed pointmultiplications or by two fixed point divisions as will later becomemore apparent. Thus, the impedance can readily be calculated basedsolely on the voltage measurements when the current is passing throughzero and its maximum values and a measure of the maximum current. Withthe availability of the impedance of the line in rectangularcoordinates, a wide range of relaying characteristics can be digitallyimplemented as will later be described and can again be readily modifiedas new conditions arise.

In FIG. 3 is shown a block diagram of voltage and current samplinghardware that can be utilized to provide a measure of the values V cos Iand V,, sin l directly. While in FIG. 3 a block diagram of hardware isshown, it should be understood that the sampling could be likewise donedirectly by a computer.

In FIG. 3 the current waveform defined by I I, sin (wt) is applied alongline 20 from the transmission line while the voltage waveform defined bythe equation V V,, sin (mt+I is applied along line 21. The currentwaveform on line 20 is applied to a conventional sample and hold circuitwhich is operative upon receiving a signal along line 22 to hold thevalue of the current which at that time is on line 20. The waveform online 20 is also fed into a zero crossing detector 23 which functions tosense the time that the value of the current is equal to zero. Each timethat the current waveform passes through zero, a pulse is output fromthe zero crossing detector 23. These pulses represented by the plot 24are applied to lines 26 and 27. The pulses from the zero crossingdetector 23 which appear on line 27 are input to a delay unit 28 whichfunctions to delay the pulses by one-fourth cycle (11/2). These delaypulses represented by the plot 29 are applied along line 30 to thesample and hold device 31 and along line 32 to the sample and holddevice 33. From a consideration of plots 25, 29 and 24, it can be seenthat the delay pulses represented by plot 29 occur when the current isat its maximum value, while the nondelay pulses 24 occur when thecurrent passes through zero.

Since the delayed pulses appearing on line 30 are applied along line 22to the sample and hold unit 31, the sample and hold unit 31 will sampleand hold the maximum current values. The output of sample and hold unit31 is applied along line 36 to the A/D converter of the computer. Thewaveform appearing on line 36 is illustrated by the plot 37. From aconsideration of the plot 37, it can be seen that the output on line 36moves between the minus maximum current value and the plus maximumcurrent value which correspond as per the previous discussion with r and+r 3 respectively. The nondelay pulses appearing on line 26 are againdelayed by means of a delay unit 38 and after the delay has timed outthe computer will be interrupted as will later be described. The delay38 is provided to prevent the computer from being interrupted prior toall the samples being completed and stored in memory.

The delay pulsed on line 30 which are applied along line 32 to thesample and hold unit 33, as previously described, occur when the currentis at its maximum values. Thus, they activate the sample and hold unit33 whenever the current is at its maximum value which, as previouslydiscussed, will provide a direct measurement of V cos I both positiveand negative. The output from the sample and hold unit 33 is appliedalong line 40 and is illustrated in plot 41. From a consideration ofplot 41, it can be seen that the output on line 40 moves from V,,, cos bto +V,,, cos D each time that a pulse appears on line 32. These valuescorrespond as previously described with r and -l-r respectively.

The nondelay pulses appearing on line 26 are also applied along line 42to the sample and hold unit 43 which receives the voltage waveform V sinmt-lb. Thus, the sample and hold unit 43 will sample and hold thepotential appearing on line 21 when the current on line 20 passesthrough zero. As previously described, this potential is equal to V sinCI Thus, the output on line 44 from the sample and hold unit 43, willmove between V,,, sin I and +V sin CD as illustrated in plot 45. Thesevalues correspond to -r and +R respectively.

Refer next to FIG. 4 which is a generalized block diagram of the controlsteps which would occur if a computer in a substation were interruptedby means, of, for instance, a signal on line 50 from the delay unit 38of FIG. 3. An interrupt action is described here since the usualcomputer will be occupied the majority of the time either controlling anumber of other lines or will be occupied in doing other tasks. Theinterrupt procedure hereinafter described is that of an IBM* TrademarkInternational Business Machines Corporationl80 System. When theinterrupt occurs, as indicted in block I, the initial housekeeping isperformed including the masking of the I/O, storing the contents of theinstruction register. storing the contents of the index register andstoring of status. When this has been done an exit is made to block 2wherein the address of the routine for the interrupt is generated andwhen this is accomplished exit is made to block 3. In block 3 the valueof the maximum current I,,, is compared with the threshold current I andin the event that l,, is less than I", exit is made to block 8 where theexit housekeeping is performed as indicated. In the event that l,,, isgreater than I," exit is made to block 4 where r= V,,, cos b/l,,, iscalculated and then exit is made to block 5 where X V," sin wi iscalculated. Since as indicated, I,,, is in memory, these values are thenstored and as indicated in block 6 the relay characteristic isimplemented and the impedance calculated in block 5 is compared with therelay characteristics in block 6 and in the event that no fault isdetected, exit to the housekeeping block 8 is made and if there is afault the circuit breaker is tripped. The above general flow chart willbe described in detail in conjunction with FIG. 6 which provides a stepby-step move through this flow chart.

To facilitate an understanding of the detailed flow chart of FIG. 6reference should be made to FIGS. 5a and 5b which will facilitate anunderstanding of the steps taken in blocks 4, 5 and 6 which result in acomparison of the relay characteristics with the calculated apparentimpedance. In FIG. 5a there is shown a circular area indicated asrelaying action. If the apparent impedance falls within this zone, thecircuit breaker should operate. From a consideration of FIG. 5a it canbe seen that the center of the circle has been offset from the zerocoordinates such that the circle lies primarily in the first quadrant.The offset in the X-direction is by an amount equal to V and in theR-direction by an amount equal to U. The impedance is represented by Zand, consequently, by computation of W, a straightforward comparison canbe made to determine ifW is greater than or less than D. If W is greaterthan D, no relaying action should take place, while if W is less than D,relaying action should occur. That is, it can be seen that W (R-U (XV)and then g In FIG. 5b is shown a straight line relay characteristicwhich approaches the ideal relay characteristic which should beimplemented but which heretofore has been difficult to obtain since theonly way to accomplish it has been through the use of blinders, addedrelays etc.

In FIG. 5b the boundaries of the relay characteristic are defined by theline P P X+R; the line W, W,X+R; the R- axis and X,,,. If the apparentimpedance falls within this zone, relay action must take place. If itfalls anywhere outside of this zone no action is taken. Theimplementation of this relay characteristic and comparison of itsboundaries with the apparent impedance as represented in coordinate formwill be considered in detail in conjunction with FIG. 6.

In FIG. 6 is shown a detailed listing of the steps which are taken toimplement the subject control technique by means of an interruptprocedure on a programmed general purpose computer. Upon receiving aninterrupt along line 50 the interrupt procedure will be entered into. Inthis procedure as indicated in Block I, the initial housekeeping istaken care of which includes the masking of the I/O which prevents anymore interrupts from being accepted by the processor. The contents ofthe instruction register, the index register, the accumulator and thequotient register along with the. status, are stored and then in block 2the address of the subroutine which is to be processed is generated.Here the address associated with the particular interrupt is loaded intothe accumulator and shifted and the number of shifts required for a onebit to come out of the accumulator is counted and this number thencontrols the branch. Depending upon which shift resulted in a l, aparticular address will be branched to and the instruction register willbe loaded with the proper instruction to initiate the subroutine. Exitis then made to block 3 and I,, is loaded into the accumulator and acompare made with I As part of the compare instruction the address of I0 which had previously been stored in memory is obtained such that I,,can be compared with I,,,. If I, is greater than 1, exit is made toblock 8 where the exit housekeeping is accomplished such that thecomputer can enter into another routine. If I,, is less than I,,,, block4 is entered irito. Inthis block I,,, is first loaded into theaccumulator and it is then inverted and I is then stored into aparticular address for temporary storage. Next, the contents of theaccumulator which holds l/I are multiplied by V,,, cos 1 which equals R,and R is then stored into a temporary address. specified by thesubroutine. Block 5 is then entered into and l/I,, which had beentemporarily stored is then brought into the accumulator and multipliedby V,,, sin 1 which yields X and X is then stored. Exit is then made toblock 6 where V is subtracted from the contents of the accumulator (X)to yield the quantity X V which is then stored into a particular addressin memory for temporary storage. The contents of the accumulator, X Vare then squared and stored in a temporary location in memory and R isloaded into the accumulator and U is subtracted from it. R U is thenstored and R U is squared and then added to (X V) and this quantitycom-' pared with D In the event that the contents of the accumulator aregreater than D no action is taken. In the event that D? is greater thanthe quantity in the accumulator, the circuit breaker will be tripped asindicated in block 7.

Exit is then made again to the exit housekeeping block 8' where thecontents of the various registers are reloaded and the 1/0 is unmaskedsuch that additional interrupts can be accepted.

As indicated in FIG. 6, an alternate relay characteristic is shown. Thisblock contains the steps which will be taken toimplement the relaycharacteristic illustrated in FIG. 5b. Here again, X will be in theaccumulator and X is compared with zero and if X is less than zero exitis then made to block 8 to the exit housekeeping and if not, X is thencompared with X,,,,, and in the event that X is greater than X exit isagain to the exit housekeeping block 8. In the event that X is less thanX,,,,

R is loaded into the accumulator and multiplied by P, and X is addedinto it and this quantity is then compared with P and if this quantityis less than P,,, exit is then made to block 8 while if this quantity isgreater than P,,, R is loaded into the accumulator and multiplied by Wand X is added into it and this quantity compared with W, and in theevent that this quantity is greater than W exit is made to the exithousekeeping block 8 and in the event that the quantity is less than Wthe breaker is tripped.

In summary, there has been provided a relaying control system whereinthe apparent impedance of a transmission line is determined withoutresort to calculations of trigonometric functions and this impedance isthen compared in a straightforward manner to specified relaycharacteristics such that control action can be taken in the event thatthe apparent impedance falls within the predetermined danger impedancezone. In this technique no mechanism is required for the determinationof the time that the zero crossings of the cur-* rent and voltage differalong with the consequent conversion of this time to phase angle andsubsequent conversion of the I phase angle to sine and cosine values forthe determinationof impedance. Instead, in this technique directreadings of the voltage at the time the current crosses through zero andthe voltage when the current is maximum are utilized to determine theapparent impedance. Through use of this technique the central dispatchercan alter the relay characteristic to conform with his particularcontrol strategy and implement relay characteristics which heretoforehave not been economically feasible to implement.

While the invention has been particularly shown and described withreference to a preferred embodiment thereof, it will be understood bythose skilled in the art that various changes in the form and detailsmay be made therein without departing from the spirit and scope of theinvention.

We claim:

1. A method of controlling the operation of breakers in a transmissionline comprising the steps of:

sampling measurement of the maximum current on said line at least onceeach cycle;

sampling measurements of the voltage on said line for each said breakerat predetermined instances during each cycle;

interrupting a computer after a set of said sampling measurements havebeen made for a breaker to supply said set of measurements thereto;

comparing, by said computer, said supplied maximum current measurementto a predetermined level;

calculating, by said computer from said supplied measurements, theapparent impedance seen by each of said breakers, said calculationoccurring in response to said current comparison step indicating thatsaid maximum current exceeds said predetermined level;

implementing desired relay characteristics for each of said breakers insaid computer;

comparing, by said computer, the relay characteristics of each of saidbreakers with its associated apparent impedance; and

opening any of said breakers having an associated apparent impedancewhich said characteristics comparison step indicates falls within itsassociated relay characteristics.

2. The method of claim 1 wherein said voltage sampling step additionallycomprises: sampling at such predetermined instances during each cyclethat the sampled measurements are of the quantities V, cos D and V,,,sin I 3. The method of claim 2 wherein said characteristics comparisonstep comprises: sequentially comparing, by said computer, each of theboundaries of each of said relay characteristics with its associatedimpedance and upon said comparison indicating that said impedance fallsoutside of any of said associated boundaries, taking no breaker action.

4. The method of claim 1 wherein said voltage sampling step additionallycomprises:

sampling measurement, for each of said breakers, of the voltage on saidline when the current is at its maximum value, thereby measuring thequantity V,, cos 4 and of the voltage on said line when the current iszero, thereby measuring the quantity V cos 1 5. The method of claim 4wherein said characteristics comparison step comprises:

sequentially comparing, by said computer, each of the boundaries of eachof said relay characteristics with its associated impedance and uponsaid comparison indicating that said impedance falls outside of any ofsaid associated boundaries, taking no breaker action. 6. The method ofclaim 5 wherein said calculation step additionally comprises:

calculating said apparent impedance by dividing each of said suppliedquantities V,, cos d and V,,, sin b by said maximum current. i 7. Themethod of claim 6 wherein said interruption step ad ditionallycomprises:

the quantities V,,, cos l V,,, sin (0 for each of said breakers and themaximum current measurement in said computer such that subsequentquantities are written over previous quantities so that the lastmeasured quantities only are available.

1. A method of controlling the operation of breakers in a transmissionline comprising the steps of: sampling measurement of the maximumcurrent on said line at least once each cycle; sampling measurements ofthe voltage on said line for each said breaker at predeterminedinstances during each cycle; interrupting a computer after a set of saidsampling measurements have been made for a breaker to supply said set ofmeasurements thereto; comparing, by said computer, said supplied maximumcurrent measurement to a predetermined level; calculating, by saidcomputer from said supplied measurements, the apparent impedance seen byeach of said breakers, said calculation occurring in response to saidcurrent comparison step indicating that said maximum current exceedssaid predetermined level; implementing desired relay characteristics foreach of said breakers in said computer; comparing, by said computer, therelay characteristics of each of said breakers with its associatedapparent impedance; and opening any of said breakers having anassociated apparent impedance which said characteristics comparison stepindicates falls within its associated relay characteristics.
 2. Themethod of claim 1 wherein said voltage sampling step additionallycomprises: sampling at such predetermined instances during each cyclethat the sampled measurements are of the quantities Vm cos phi and Vmsin phi .
 3. The method of claim 2 wherein said characteristicscomparison step comprises: sequentially comparing, by said computer,each of the boundaries of each of said relay characteristics with itsassociated impedance and upon said comparison indicating that saidimpedance falls outside of any of said associated boundaries, taking nobreaker action.
 4. The method of claim 1 wherein said voltage samplingstep additionally comprises: sampling measurement, for each of saidbreakers, of the voltage on said line when the current is at its maximumvalue, thereby measuring the quantity Vm cos phi , and of the voltage onsaid line when the current is zero, thereby measuring the quantity Vmcos phi .
 5. The method of claim 4 wherein said characteristicscomparison step comprises: sequentially comparing, by said computer,each of the boundaries of each of said relay characteristics with itsassociated impedance and upon said comparison indicating that saidimpedance falls outside of any of said associated boundaries, taking nobreaker action.
 6. The method of claim 5 wherein said calculation stepadditionally comprises: calculating said apparent impedance by dividingeach of said supplied quantities Vm cos phi and Vm sin phi by saidmaximum current.
 7. The method of claim 6 wherein said interruption stepadditionally comprises: the quantities Vm cos phi , Vm sin phi for eachof said breakers and the maximum current measurement in said computersuch tHat subsequent quantities are written over previous quantities sothat the last measured quantities only are available.